We consider an experiment to search for dark sector particles in invisible (or semi-invisible) decays of neutral mesons M0 = pi 0, eta, eta', omega, f2(1270), which produced the charge-exchange reactions pi- + (A, Z) - M0 + (A, Z - 1); M0 - invisible of high-energy pions (or kaons) on a nuclei target in the NA64 experiment at the CERN SPS. This reaction chain would lead to a striking signature of the signal event-the complete disappearance of the beam energy in the setup [Phys. Rev. D 91, 015004 (2015)]. Using data obtained from the measurements at IHEP (Protvino) and Fermilab (Batavia) we show that the integral cross sections sigma for the production of the M0 s slightly deviate from the phenomenological formula sigma similar to Z2/3, where Z is the nuclei charge. In particular, we present the formulas for the differential and integral cross sections that explicitly depend on the Mandelstam and Z variables. Derived formulas are used to predict the M0 yield as a function of beam energy for several target nuclei, and to estimate the projection sensitivity for the proposed search in the dark vector portal model. Sensitivity to different decay modes of M0s is explored.